As Antarctic subglacial lake research progresses to in situ exploration an important topic is the lake's probable gas concentration. Depending on hydrological setting, subglacial lakes may contain large amounts of dissolved gas or gas trapped within clathrates. Consequently, access can be potentially dangerous due to the risk of blowout where depressurization could lead to high-speed ejection of water and gas from a borehole. We present a structured approach to assess the blowout risk in subglacial lake exploration. The approach integrates a generic event tree, applicable to open and closed hydrological systems, with site-specific expert judgment incorporating rigorous probabilistic formulations. The methodology is applied to a motivating example: Ellsworth Subglacial Lake. Judgments elicited through a formal process were provided by five experts with 88 years combined experience that, after aggregation, gave a median risk of blowout of 1 in 2186 with a lower quartile of 1 in 3433 and an upper quartile of 1 in 1341. This approach can be applied to any subglacial lake given a modicum of knowledge on its hydrological setting, as uncertainty can be captured through the elicited judgments. Additionally, the event tree analysis informs blowout mitigation strategies to reduce risk of injury or death.